Lesson 12
NYS COMMON CORE MATHEMATICS CURRICULUM
6•1
Lesson 12: From Ratio Tables to Double Number Line
Diagrams
Student Outcomes

Students create equivalent ratios using a ratio table and represent these ratios on a double number line
diagram.

Students extend and use a double number line diagram to solve ratio problems related to the real world.
Classwork
Exercise 1 (5 minutes)
Scaffolding:
Recall of prior knowledge—Ratio Tables (See attached ratio cards.)
Differentiate the activity by
choosing select cards for each
student. A ratio of 2:1 may be
easier for a struggling learner
to conceptualize, while a ratio
Each student is given a card with a ratio on it. The students move around the room in
search of other students who have ratios that are equivalent to theirs. Students with
equivalent ratios will form a group and create a ratio table, which will contain all of the
MP. equivalent ratios. As students present their ratio tables, the student audience will
2 determine the accuracy of the groups’ formations, as well as their tables. Circulate the
room as a facilitator, guiding students who are having trouble. Collect cards and direct
students back to their seats once the groups are completed.
of 3 : 2 may be more
challenging.
For more support:
Exercise 2 (7 minutes)
A guided whole-group discussion occurs as outlined below. Students are given time to
think about and discuss the following questions independently and/or with their peers and
then contribute to the whole-group discussion.
To provide more information
on this topic to support all
learners’ needs, refer to
Teacher Notes - More
Information on Soda and Sugar
for video and news-related
links.
Exercise 2
The amount of sugary beverages Americans consume is a leading health concern. For a given brand of cola, a 12-ounce
serving of cola contains about 40 grams of sugar. Complete the ratio table, using the given ratio to find equivalent ratios.
Cola (ounces)
Sugar (grams)
6
20
18
60
12
40
Answers may vary but are found by either multiplying or dividing both 12 and 40 by the same number.
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6•1
Exercise 3 (7 minutes)
Exercise 3
A 1-liter bottle of cola contains approximately 34 fluid ounces. How many grams of sugar would be in a 1-liter bottle of
the cola? Explain and show how to arrive at the solution.
Cola (ounces)
6
12
18
30
36
Sugar (grams)
20
40
60
100
120
Students may use different approaches. Some students may decide to extend their tables but may realize that they do
MP. not “easily” arrive at 34 for the ounces of cola when finding equivalent ratios. After adequate time, have
3 students/groups present their predictions and methods to the class.
When eliciting students’ responses, ask probing questions as the opportunity arises, (i.e.: “So are you telling me that
since 34 ounces is between 30 and 36 ounces, the answer will be between 100 and 120 grams of sugar? Is it closer to
MP.
100 or 120? How do you know? Will the answer be a whole number? Why or why not? Can you express your answer
1
as a mixed number?”)

What are some of the challenges we face when using a table for this type of problem?

34 is not a multiple of 6, and we are counting by 6’s for the ounces of cola and by 20’s for grams of
sugar.
Example 1 (9 minutes)
Whole group instruction continues with a teacher-led illustration of using a double number
line diagram to arrive at the answer for Example 1. Discussion includes the need for two
MP. different number lines since we are comparing ounces and grams, which are not the same
5 units (1 gram is not equivalent to 1 ounce). Students record the following illustration on
the double number line reproducible.
0
6
12
18
24
30
0
20
40
60
80
100

Fluency Exercise to Reinforce
Understanding:
Students can practice skipcounting aloud for each
number line to understand the
concept of scale.
34 36 cola (ounces)
?
120 sugar (grams)
What is the scale we are using on each number line?

6 for cola and 20 for sugar
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Date:
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Lesson 12
NYS COMMON CORE MATHEMATICS CURRICULUM
Show on the cola number line that 34 ounces is
or of the way between 30 and 36. The answer for grams of sugar
will be or of the way between 100 and 120. Since the intervals are by 20, to determine the answer, find
add it to 100. Students may choose to use
6•1
of 20 and
instead of .
Elicit student volunteers to show the math process and work using each of the two fractions. Students should see that
the answers will be the same regardless of which fraction was used.
OR
grams of sugar
grams of sugar
Exercise 4 (7 minutes)
Exercise 4
A school cafeteria has a restriction on the amount of sugary drinks available to students. Drinks may not have more than
25 grams of sugar. Based on this restriction, what is the largest size cola (in ounces) the cafeteria can offer to students?
0
6
?
25
0
20
30
12
18 cola (ounces)
40
60 sugar (grams)
35
My estimate is between 6 and 12 ounces but closer to 6 ounces. I need to find ¼ of 6 and add it to 6.
A
ounce cola is the largest size that the school cafeteria can offer to students.
After students have ample time to create their double number line diagram and answer the question, encourage
students to present their thought process to the class.
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6•1
Exercise 5 (time permitting)
Exercise 5
Shontelle solves three math problems in four minutes.
a.
Use this information to complete the table below.
Number of
Questions
Number of
Minutes
b.
3
6
9
12
15
18
21
24
27
30
4
8
12
16
20
24
28
32
36
40
Shontelle has soccer practice on Thursday evening. She has a half hour before practice to work on her math
homework and to talk to her friends. She has 20 math skill-work questions for homework, and she wants to
complete them before talking with her friends. How many minutes will Shontelle have left after completing
her math homework to talk to her friends?
Use a double number line diagram to support your answer, and show all work.
Step 1:
Step 2:
Step 3:
Shontelle can talk to her friends for
minutes.
Closing (5 minutes)

Have students complete the 3-2-1 Activity.

Name three different ways you can represent a group of equivalent ratios.

Ratio Table, Tape Diagram, Double Number Line Diagrams

Share two things you learned about Double Number Line Diagrams.

Tell one thing you want to know more about from today’s lesson.
Lesson Summary
Double Number Line Diagram: a tool used for understanding the equivalence of two related numbers. It is called
“double” because each mark on the line has two numbers matched to it. The top row of numbers describes the
whole represented by the line in one way, and the bottom row describes the whole represented by the line in
another way. Because the whole line is the same, it is possible to see the equivalences between the rows of
numbers at any point on the line.
Exit Ticket (5 minutes)
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Additional Teacher Notes
More Information on Soda and Sugar:
Video: http://www.cnn.com/2013/01/14/health/coke-obesity
Video: http://www.teachertube.com/viewVideo.php?video_id=13788
http://www.sugarstacks.com/beverages.htm
http://www.cdc.gov/features/healthybeverages/
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Lesson 12
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
6•1
Date____________________
Lesson 12: From Ratio Tables to Double Number Line Diagrams
Exit Ticket
Kyra is participating in a fundraiser Walk-a-Thon. She walks 2 miles in 30 minutes. If she continues to walk at the same
rate, determine how many minutes it will take her to walk 7 miles. Use a double number line diagram to support your
answer.
Lesson 12:
Date:
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From Ratio Tables to Double Number Line Diagrams
4/1/14
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6•1
Exit Ticket Sample Solution
The following solutions indicate an understanding of the objectives of this lesson:
Kyra is participating in a fundraiser Walk-a-Thon. She walks 2 miles in 30 minutes. If she continues to walk at the same
rate, determine how many minutes it will take her to walk 7 miles. Use a double number line diagram to support your
answer.
Miles
2
4
6
30
60
90 105 120
7
8
Minutes
It will take Kyra 105 minutes to walk 7 miles.
Problem Set Sample Solutions
1.
While shopping, Kyla found a dress that she would really like, but it costs $52.25 more than she has. Kyla charges
$5.50 an hour for babysitting. She wants to figure out how many hours she must babysit to earn $52.25 to buy the
dress. Use a double number line to support your answer.
9.5 hours
2.
Frank has been driving at a constant speed for 3 hours, during which time he traveled 195 miles. Frank would like to
know how long it will take him to complete the remaining 455 miles, assuming he maintains the same constant
speed. Help Frank determine how long the remainder of the trip will take. Include a table or diagram to support
your answer.
7 hours
Lesson 12:
Date:
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6•1
7 to 4
28:16
3 to 2
35:20
3 to 8
30:80
6 to 16
12:32
5 to 1
45:9
15 to 3
2 to
Lesson 12:
Date:
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From Ratio Tables to Double Number Line Diagrams
4/1/14
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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Lesson 12
NYS COMMON CORE MATHEMATICS CURRICULUM
6•1
3 to 4
9:16
1 to 2
15:20
3 to 6
30:60
1 to 2
4:8
2 to 1
44:22
18:9
1 to
Lesson 12:
Date:
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From Ratio Tables to Double Number Line Diagrams
4/1/14
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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Lesson 12
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6•1
1 to 6
8:48
6 to 36
5:30
9 to 4
36:16
3 to
18:8
7 to 6
42:36
21 to 8
Lesson 12:
Date:
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3 to 3
From Ratio Tables to Double Number Line Diagrams
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6•1
Double Number Line Reproducible
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Date:
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